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The letter tiles C, A, R, E

𝐶
,

𝐴
,

𝑅
,

𝐸
, and S
𝑆
are placed in a box. Without looking, Jorelle picks a letter tile from the box and records the result before placing it back. He repeats the procedure 100 times and observes the following results:

The table presents the frequency of occurrences for letters C, A, R, E, and S when Jorelle picks them from the box.
Outcomes C A R E S
Frequency 20 25 30 10 15
Based on the observed frequency, develop a probability model for this experiment. Express the probability in decimal form, rounded to the nearest hundredth.

(1 point)
Responses

X C A R E S
P(X) 0.20 0.30 0.25 0.10 0.15
X C A R E S P(X) 0.20 0.30 0.25 0.10 0.15

X C A R E S
P(X) 0.25 0.25 0.35 0.15 0.15
X C A R E S P(X) 0.25 0.25 0.35 0.15 0.15

X C A R E S
P(X) 0.20 0.25 0.30 0.10 0.15
X C A R E S P(X) 0.20 0.25 0.30 0.10 0.15

X C A R E S
P(X) 0.02 0.03 0.03 0.01 0.015

1 answer

To develop a probability model based on the observed frequencies for the letters C, A, R, E, and S, we can calculate the probability of each letter by dividing the observed frequency of each letter by the total number of trials (which is 100 in this case).

Here's how to calculate the probabilities:

  • For C: \[ P(C) = \frac{20}{100} = 0.20 \]

  • For A: \[ P(A) = \frac{25}{100} = 0.25 \]

  • For R: \[ P(R) = \frac{30}{100} = 0.30 \]

  • For E: \[ P(E) = \frac{10}{100} = 0.10 \]

  • For S: \[ P(S) = \frac{15}{100} = 0.15 \]

Now, let's summarize the results in the probability model:

X      C     A     R     E     S
P(X)  0.20  0.25  0.30  0.10  0.15

Therefore, the correct response based on the observed frequency is:

X C A R E S
P(X) 0.20 0.25 0.30 0.10 0.15